1. If the original flight into MIA was from the EU, then EC 261/2004 will apply and OP should come back with those details. If not, put the Regulation aside as it is not applicable.

2. Everything else is simply a matter of reasonableness. Hotel, food & local transport. But, consequential damages are expressly excluded from their contract with AA (and would be with pretty much all carriers for the reasons described upthread).

3. That leaves two things. While no compensation is due, it is possible that AA will grant some form of customer service gesture, e.g. miles or credit. It will not link that to the hotel night, but it is something. Also, most properties are very understanding of these sorts of occurrences and will often work with customers to extend a stay, refund points or do something else. They key is to call the property directly (not a toll-free reservations line) ASAP as the earlier the call comes in, the more likely the property is to find a taker for the room. Finally, while award stays can be tricky, many travel insurance policies pay out a set dollar amount after a given delay. Thus, while the points might be gone, there would be some cash.